Question

Find the point of contact in a circle.

Answer 1

Hint: The line which touches the circle at one point on its circumference is known as the tangent to the circle. The point of intersection of tangent with the circle is the point of contact.

Complete step by step solution:
The centre of the circle lies in the middle of the circle. In the above figure, O is the centre of the circle and is equidistant from all points on the circumference of the circle.
The line which intersects the circle cannot be the tangent to circle as tangent touches the circle but does not cut it. Instead, the line intersecting the circle can be chord or secant.
The line CA is the tangent line to the circle as it touches the circle at one point. The tangent to circle is also perpendicular to the radius of the circle at the point of intersection. By perpendicular, the meaning to be denoted is that the angle made at the intersection of tangent and radius is $90{}^{\circ }$.
The line going through points A and C in the above figure is touching the circle at point A on the circumference of the circle. This indicates the point of contact in the circle is point A. C is point outside the circle as it lies out of the boundary of the circle.

Note:
> The centre of the circle is always inside the circle.
> The distance between the centre of circle and any point on boundary (or circumference of circle) is known as the radius of circle.